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Coronagraphs (together with starshades) are an important tool to directly image and characterize exoplanets, and enable the search for biomarkers in reflected light on potentially habitable worlds. Their performance and efficiency has steadily been improving over the past several decades, but has not yet reached performance limits. In particular, the expected exoplanet yield for missions such as the Astro2020-recommended “IR/O/UV Flagship” can still be improved by factors of at least 2-3, simply by continued improvements in coronagraph performance, before they plateau due to physics limits. One possible architecture that can enable at least a part of this improvement is the Phase-Induced Amplitude Apodization Complex Mask Coronagraph (PIAACMC). Itoffersthe advantages of high throughput, small inner working angle (IWA),and almost noloss inPSF sharpness, and natively supports obstructed and segmented apertures, which is essential to the Astro2020 “IR/O/UV Flagship”mission. Historically, key disadvantages of PIAA have been poor tolerance to stellar angular sizes and maturity, but latest designs and demonstrations have made significant strides in this respect.In this paper, we present the current status and overview of our program to mature the PIAACMC technology. We first review PIAACMC designs for LUVOIR-A and B, which resultedin improved expected yield of Exo-Earths relative tothe baselines for both mission concepts. In particular, for LUVOIR-B, the yield improves from 28 to 42due to improvedtolerance to stellar angular size in our design. The improvement in yield is marginal for LUVOIR-A, but our design enables detecting planets around smaller diameter stars (nearby K-dwarfs and/or farther FG stars). We also describe our modeling and vacuum demonstrationsfor the LUVOIR-A aperture(which is more challengingthan LUVOIR-B due to the central obstruction).The demonstration included a LUVOUR-A pupil mask, an on-axis PIAA set of 2 mirrors with central holes, a Boston Micromachines DM, a patterned CMC mask, Lyot stop, and supporting masks and optics. Demonstrations were conducted at JPL’s High Contrast Imaging Testbed (HCIT) using several characterization andwavefront control techniques (primarily standard EFC, several experimental techniques were attempted, as well as speckle nulling). So far, our results include 1.9e-8 raw contrast in 10% broadband light between 3.5 and 8 l/D; 4.1e-8 and 1.6e-9 coherent contrasts in monochromatic light between 2-4 and 4-8 l/D, respectively. We also present measurements and analysis of sensitivity to tip/tilt jitter and stellar angular size. Finally, we compare our test results to models, present an analysis of our limiting factors, and explorefuture prospectsfor improvement based on validated models.